A390077 Decimal expansion of the negated value of psi''(1/6).

4, 3, 3, 5, 9, 2, 1, 4, 2, 6, 3, 0, 3, 1, 5, 5, 6, 5, 1, 3, 1, 3, 1, 5, 4, 1, 9, 1, 9, 4, 7, 3, 9, 7, 6, 7, 6, 0, 1, 9, 7, 8, 4, 2, 8, 4, 3, 2, 5, 6, 1, 9, 1, 7, 6, 3, 8, 3, 6, 2, 1, 6, 4, 8, 5, 6, 2, 4, 9, 6, 6, 0, 5, 4, 2, 2, 0, 6, 5, 1, 6, 8, 5, 8, 9, 1, 0, 3, 6, 0, 6, 5, 8, 8, 5, 5, 1, 6, 9, 6, 1, 3, 4, 9, 8, 7, 1, 5, 7

Offset

3,1

Comments

Decimal expansion of the absolute value of the second derivative of the digamma function at 1/6.

Links

Paolo Xausa, Table of n, a(n) for n = 3..10000

E. D. Krupnikov and K. S. Kölbig, Some special cases of the generalized hypergeometric function _{q+1}F_q, J. Comp. Appl. Math. 78 (1997) 79-95.

Index entries for sequences related to the digamma function

Formula

Equals 182*zeta(3) + 4*sqrt(3)*Pi^3 = 2*6^3*A377560.

Example

psi''(1/6) = -433.59214263031556513131541919473976760197842843256...

Maple

-182*Zeta(3)-4*sqrt(3)*Pi^3 ; evalf(%) ;

Mathematica

First[RealDigits[PolyGamma[2, 1/6], 10, 100]] (* or *)
First[RealDigits[182*Zeta[3] + 4*Sqrt[3]*Pi^3, 10, 100]] (* Paolo Xausa, Nov 17 2025 *)

Prog

(PARI) -psi''(1/6) \\ Michel Marcus, Oct 23 2025

Crossrefs

Cf. A222457 (psi(1/6)), A390076 (psi'(1/6)).

Sequence in context: A372049 A154913 A154915 * A238376 A237197 A006994

Adjacent sequences: A390074 A390075 A390076 * A390078 A390079 A390080

Keyword

cons,nonn

Author

R. J. Mathar, Oct 23 2025

Status

approved